Wednesday, December 14, 2011

Financial Physics: "Power laws in finance"

From The Physics of Finance:

My latest column
in Bloomberg looks very briefly at some of the basic mathematical
patterns we know about in finance. Science has a long tradition of
putting data and observation first. Look very carefully at what needs to
be explained -- mathematical patterns that show up consistently in the
data -- and then try to build simple models able to reproduce those
patterns in a natural way.

This path has great promise in economic finance, although it hasn't been
pursued very far until recently. My Bloomberg column gives a sketch of
what is going on, but I'd like to give a few more details here and some
links.

The patterns we find in finance are statistical regularities -- broad
statistical patterns which show up in all markets studied, with an
impressive similarity across markets in different countries and for
markets in different instruments. The first regularity is the
distribution of returns over various time intervals, which has been
found generically to have broad power law tails -- "fat tails" --
implying that large fluctuations up or down are much more likely than
they would be if markets fluctuated in keeping with normal Gaussian
statistics. Anyone who read The Black Swan knows this.

This pattern has been established in a number of studies over the past
15 years or so, mostly by physicist Eugene Stanley of Boston University
and colleagues. This paper
from 1999 is perhaps the most notable, as it used enormous volumes of
historical data to establish the fat tailed pattern for returns over
times ranging from one minute up to about 4 days. One of the most
powerful things about this approach is that it doesn't begin with any
far reaching assumptions about human behaviour, the structure of
financial markets or anything else, but only asks -- are there patterns
in the data?...MORE

...The
quantitative aspirations of economists and financial analysts have for
many years been based on the belief that it should be possible to build
models of economic systems - and financial markets in particular - that
are as predictive as those in physics.

While this perspective has
led to a number of important breakthroughs in economics, "physics envy"
has also created a false sense of mathematical precision in some cases.
We speculate on the origins of physics envy, and then describe an
alternate perspective of economic behavior based on a new taxonomy of
uncertainty.

We illustrate the relevance of this taxonomy with
two concrete examples: the classical harmonic oscillator with some new
twists that make physics look more like economics, and a quantitative
equity market-neutral strategy. We conclude by offering a new
interpretation of tail events, proposing an "uncertainty checklist" with
which our taxonomy can be implemented, and considering the role that
quants played in the current financial crisis...